Simplify the following expression: $k = \dfrac{30a^2 - 20ca}{40a^2 + 60ba} + \dfrac{40ba + 10ca}{40a^2 + 60ba}$ You can assume $a,b,c \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{30a^2 - 20ca + 40ba + 10ca}{40a^2 + 60ba}$ $k = \dfrac{30a^2 - 10ca + 40ba}{40a^2 + 60ba}$ The numerator and denominator have a common factor of $10a$, so we can simplify $k = \dfrac{3a - c + 4b}{4a + 6b}$